Bayesian Analysis in Critical Care Medicine

We commend Zampieri and colleagues (pp. 423–429) for their study presented in this issue of the Journal (1), in which they conducted a thoughtful Bayesian reanalysis of results from a trial conducted within a developing research network to assess an intervention with broad applications (2). The premise of the ANDROMEDA-SHOCK trial was to compare a novel peripheral perfusion–based resuscitation approach using capillary refill time with a more conventional lactate-based approach to guide resuscitation (2). The trial reported an 8.5% reduction in absolute mortality but failed to reject the null hypothesis, motivating Zampieri and colleagues to repeat the analysis from a Bayesian perspective, which showed a consistently high probability that the intervention improved mortality across a range of prior beliefs. This reanalysis gives us an opportunity to consider the usefulness of a Bayesian approach in critical care medicine.

Bayesian analysis can be intimidating for many clinicians because it uses unfamiliar terms and takes a fundamentally different approach to drawing statistical conclusions from data as compared with frequentist analysis. However, any increased familiarity that clinicians feel toward conventional (frequentist) statistics is likely a false comfort, given the well-documented problems with the use of frequentist statistics in contemporary science (3). Bayesian analysis is sometimes proposed as an improved way to draw statistical conclusions from clinical data because it allows for the incorporation of information external to the trial (prior information) and makes it easy to answer the question, what is the probability that the intervention has a benefit of at least X%? Incorporating prior information in critical care trials is helpful because critical illness is rare, and so it may be wise to use all available information when analyzing a trial. Calculating the probability of benefit is also useful in critical care medicine, where morbidity and mortality are common, and so it may be helpful to identify interventions where frequentist analysis has failed to reject the null hypothesis but the probability of benefit is still high, as in the case of ANDROMEDA-SHOCK.

One common clinical reasoning approach that is similar to Bayesian analysis is the use of diagnostic tests. Consider a patient with shortness of breath and a swollen leg. A clinician may suspect a pulmonary embolism based on the clinical data (analogous to prior information) and order a diagnostic test such as a D-dimer. The D-dimer test result (analogous to a clinical trial or experiment) will have a different likelihood depending on whether or not a patient actually has a pulmonary embolism—a negative test is very unlikely if a patient does have a pulmonary embolism. The clinician then combines the likelihood of the obtained result with the prior probability of having a pulmonary embolism to compute an updated probability (posterior probability) that this individual has a pulmonary embolism. Clinicians do not make these calculations explicitly, but instead perform them intuitively. By analogy, a Bayesian analysis of a clinical trial combines prior information (analogous to the clinical data that prompts investigation) with the likelihood of the observed trial data (analogous to the result of the diagnostic test) to compute a posterior probability of benefit (analogous to the posttest probability of having the disease).

Prior information is an important component of Bayesian analysis that requires thorough justification and is not included in frequentist analyses. The prior information itself is summarized in the form of a probability distribution, which is an equation that can be used to calculate the chance that an intervention will have benefit. Justification for a prior distribution can consider aspects of the trial design that were not accounted for in the analysis, prior clinical research relating to the specific topic or the general area, and mechanistic information justifying the plausibility of a causal relationship. Relevant prior data can be incorporated into a prior distribution but given less weight if the information is not perfectly pertinent to the situation at hand. For example, in their Bayesian reinterpretation of a recent trial evaluating the use of extracorporeal membrane oxygenation in acute respiratory distress syndrome, Goligher and colleagues used priors based on a meta-analysis of similar studies, giving these studies weights between 0% and 100% (4). Another approach to constructing priors involves querying experts to build empiric distributions, which can yield complex distributions that are not described by a closed form equation (5). Different scientists may weight different aspects of the prior information with more or less importance, yielding some variation in prior distributions.

Just as Zampieri and colleagues have done, a thorough Bayesian analysis should consider multiple prior distributions representing different ways of synthesizing prior information into a distribution, so that readers can see the impact of prior information on the results of the analysis (6). In their Bayesian reanalysis, Zampieri and colleagues selected four priors for the odds ratio, labeling them optimistic, neutral, null, and pessimistic. The optimistic prior encodes belief that the therapy will have clinical benefit, the pessimistic prior encodes belief that the therapy will cause harm, and the neutral prior encodes belief that extremes of benefit and harm are both unlikely. Based on particular details of the mechanism, background literature, and trial, each reader can decide whether the optimistic, neutral, or pessimistic prior best represents their view of the prior information and see how that impacts the results.

The ability to adjust prior distributions based on subjective information is a true strength of Bayesian analyses, even though it is sometimes characterized as a weakness. Clinicians are not swayed by irrational prior distributions that, for example, violate the principles of equipoise. In analyses of frequentist trials, the same arguments used to justify prior distributions regarding mechanism, trial design, prior research, and external validity appear in the Discussion section instead of the Methods section, and neither authors nor critics are required to quantify the effect of the study’s limitations or areas of controversy on their results. Bayesian analyses with thoughtful prior distributions provide an opportunity for clinicians to quantitatively and transparently incorporate multiple modes of evidence and context into their interpretation of randomized trial data, with the hope of making the best possible decisions for critically ill patients. Broader adoption of Bayesian analyses in critical care medicine trials will promote transparency in combining all available sources of data for clinical decision-making.